Let me start by answering your 3 questions (the last part in your question).
There are 5 Project Management Maturity Levels:
Project Management Maturity Level 1: Ad-hoc. We do project management when we need it.
Project Management Maturity Level 2: Planned. We plan for projects.
Project Management Maturity Level 3: Managed. Formal project management is applied in some departments, but not all.
Project Management Maturity Level 4: Integrated. Formal project management is applied in all departments.
Project Management Maturity Level 5: Sustained. Formal project management is applied across the organization, and projects affect and are affected by the organization's overall strategy (In other words, Program Management exists at this level).
Knowing the PM maturity level of a company is an important factor to assess the efficiency of the company, and hence it's mostly used by business people.